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Chapter: Mensuration· Mathematics Part 2 (Geometry)

Asked in: March 2024 board paper (square-minus-sector shaded region of the same kind in March 2026)In the figure, □ABCD is a square and a circle is inscribed in it. All sides of the square touch the circle. If AB = 14 cm, find the area of the shaded…

Asked in: March 2024 board paper (square-minus-sector shaded region of the same kind in March 2026)

In the figure, □ABCD is a square and a circle is inscribed in it. All sides of the square touch the circle. If AB = 14 cm, find the area of the shaded region.

[Figure: Square ABCD of side 14 cm with a circle touching all four sides; the four corner regions outside the circle are shaded.]

Solution: Area of square = (____)\(^2\) (Formula) = \(14^2\) = ____ cm\(^2\)

Area of circle = ____ (Formula) \(= \dfrac{22}{7} \times 7 \times 7 = 154\) cm\(^2\)

(Area of shaded portion) = (Area of square) – (Area of circle) = 196 – 154 = ____ cm\(^2\)

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Answer: Area of shaded region = 42 cm\(^2\)

Area of square \(= (\text{side})^2 = 14^2 = 196\) cm\(^2\).

The circle touches all sides, so its diameter = side = 14 cm and r = 7 cm. Area of circle \(= \pi r^2 = \dfrac{22}{7} \times 7 \times 7 = 154\) cm\(^2\).

Area of shaded region = 196 – 154 = 42 cm\(^2\).

Blanks: side; 196; \(\pi r^2\); 42.

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